Theorem 2.1  (Vogan [1]})
Let \(p=(x, \lambda , \nu )\)  be the atlas final parameter of an irreducible \((\mathfrak {g}, K)\) -module \(\pi \) .
Let \(S(x)\)  be the support of \(x\) , and \(\mathfrak {q}(x)\)  be the \(\theta \) -stable parabolic subalgebra given by the pair \((S(x), x)\) , with Levi factor \(L(x)\) .
Then \(\pi \)  is cohomologically induced, in the weakly good range,
from an irreducible \((\mathfrak {l}, L(x)\cap K)\) -module \(\pi _{L(x)}\)  with final parameter \(p_{L(x)}=(y, \lambda -\rho (\mathfrak {u}), \nu )\) , where \(y\)  is the KGB element of \(L(x)\)  corresponding to the KGB element \(x\)  of \(G\) .

